1. Technical Field
The present invention relates to a manufacturing process control method, and more particularly to a method for combining physical objects and evaluating the combining process using Polar coordinate statistical analysis.
We live in an environment with a countless number of entities that can be described as variables in a two-dimensional or three dimensional coordinate system. Spatial orientation or color are a few examples of these variables. As we seek to learn more about these entities, it is important to understand how to define these entities in their coordinate system. Presently, a method to accurately and precisely assess the mean or difference between entities (from multiple measurements of the variables) in a way that can withstand the rigor of statistical examination is lacking. The importance of accuracy and precision has significant ramifications in any area of interest where the exactness of a measurement is a requirement.
With regard to spatial orientation, a quality control inspection in a manufacturing process would require an exact measurement. For instance, if two manufactured parts are being assembled, then exact measurements may be needed to assess where a first part is in relation to a second part. Generally, an accurate and precise method for positioning comparing and/or combining a physical entity with respect to another entity has numerous applications, including laser-welding of parts, precision measurements in dentistry, color matching in the paint industry, navigation, computer circuitry, microphotography, as well as spacial orientation of space crafts, projectiles and long-range telescopes.
Any exact measurement result relies on the multiple measurements which then can be analyzed through the correct statistical analysis method. At the present time, statistical analysis is being performed under the fundamental assumption of tan .THETA.=.THETA. that is generally applied in the calculation of the approximate length of a curved path in a plane, and thus the analysis of two-dimensional and three-dimensional data are presently using a linear statistical analysis method in the Cartesian coordinate system. The principal difference between the curved length calculation and the statistic analysis of a set of two-dimensional or three-dimensional data which includes a curved distribution, is that a curved path with a continuous value allows for using straight line segments (one can imagine as short as one please), such that each set of segments makes a polygonal path that fits the curve more tightly than before and by applying an integral the smooth enough "curve" is calculated. In contrast, if the data points are such that it is impossible to set straight line segments "as short as one please", then the fundamental assumption of the integral theory can not be applied in all statistical analysis. When the statistics for the tan .THETA..noteq..THETA. data set are reported with the linear statistical analysis in the Cartesian coordinate system, tyhe reported values can only provide the approximate values. Reported values that are less than "true" will produce errors in any two- or three-dimensional spatial relationships that are being analyzed by the Cartesian approach. The magnitude of the error depends on the magnitude of the tan .THETA.-.THETA. difference per unit vector. The disadvantage in the Cartesian approach of analysis are directly related to accuracy and precision. As applied to the above-described quality control inspection application, reported values that are less than the true mean will produce errors in any two- or three-dimensional spacial relationships that are being analyzed by the Cartesian approach.
Therefore, it is desirable to provide a method for combining physical entities and evaluating the combining process using a Polar coordinate statistical analysis approach. By employing the method of the present invention, manufactured parts may be precisely assembled, an exact color match of paint can be created to match the paint of a scratched automobile, or the fit between an implant abutment and the prosthesis framework can be more accurately assessed. Regardless of the particular application, multiple measurements of variables used to describe each entity in a coordinate system are used to accurately and precisely assess the true mean. The Polar coordinate approach combines a linear statistical analysis method of the distance coordinate with a circular directional statistical analysis method on the angular coordinate(s), and thus is capable of computing the true mean values.